Computational Fluid Dynamics
(CFD)
U7AEA29
Dr. S. Senthil Kumar
Associate Professor
Dept. of Aeronautical Engineering
Vel Tech Dr. RR & Dr. SR Technical University
Avadi, Chennai
.
Outline
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What is CFD?
Why use CFD?
Where is CFD used?
Physics
Modeling
Numerics
CFD process
Resources
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What is CFD?
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What is CFD and its objective?
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Computational Fluid Dynamics
Historically Analytical Fluid Dynamics (AFD) and EFD
(Experimental Fluid Dynamics) was used. CFD has become
feasible due to the advent of high speed digital computers.
Computer simulation for prediction of fluid-flow phenomena.
The objective of CFD is to model the continuous fluids with
Partial Differential Equations (PDEs) and discretize PDEs into an
algebra problem (Taylor series), solve it, validate it and achieve
simulation based design.
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Why use CFD?
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Why use CFD?
– Analysis and Design
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Simulation-based design instead of “build & test”
– More cost effectively and more rapidly than with experiments
– CFD solution provides high-fidelity database for interrogation of
flow field
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Simulation of physical fluid phenomena that are difficult to be
measured by experiments
– Scale simulations (e.g., full-scale ships, airplanes)
– Hazards (e.g., explosions, radiation, pollution)
– Physics (e.g., weather prediction, planetary boundary layer,
stellar evolution)
– Knowledge and exploration of flow physics
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Where is CFD used? (Aerospace)
• Where is CFD used?
– Aerospace
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Appliances
Automotive
Biomedical
Chemical Processing
HVAC&R
Hydraulics
Marine
Oil & Gas
Power Generation
Sports
F18 Store Separation
Wing-Body Interaction
Hypersonic Launch
Vehicle
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Where is CFD used? (Appliances)
• Where is CFD used?
– Aerospace
– Appliances
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Automotive
Biomedical
Chemical Processing
HVAC&R
Hydraulics
Marine
Oil & Gas
Power Generation
Sports
Surface-heat-flux plots of the No-Frost
refrigerator and freezer compartments helped
BOSCH-SIEMENS engineers to optimize the
location of air inlets.
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Where is CFD used? (Automotive)
• Where is CFD used?
– Aerospace
– Appliances
– Automotive
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Biomedical
Chemical Processing
HVAC&R
Hydraulics
Marine
Oil & Gas
Power Generation
Sports
External Aerodynamics
Interior Ventilation
Undercarriage
Aerodynamics
Engine Cooling 8
Where is CFD used? (Biomedical)
• Where is CFD used?
– Aerospace
– Appliances
– Automotive
– Biomedical
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Chemical Processing
HVAC&R
Hydraulics
Marine
Oil & Gas
Power Generation
Sports
Medtronic Blood Pump
Temperature and natural
convection currents in the eye
following laser heating.
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Where is CFD used? (Chemical Processing)
• Where is CFD used?
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Aerospace
Appliances
Automotive
Biomedical
– Chemical Processing
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HVAC&R
Hydraulics
Marine
Oil & Gas
Power Generation
Sports
Polymerization reactor vessel - prediction
of flow separation and residence time
effects.
Twin-screw extruder
modeling
Shear rate distribution in twinscrew extruder simulation
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Where is CFD used? (HVAC&R)
• Where is CFD used?
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Aerospace
Appliances
Automotive
Biomedical
Chemical Processing
Streamlines for workstation
ventilation
– HVAC&R
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Hydraulics
Marine
Oil & Gas
Power Generation
Sports
Mean age of air contours indicate
location of fresh supply air
Particle traces of copier VOC emissions
colored by concentration level fall
behind the copier and then circulate
through the room before exiting the
exhaust.
Flow pathlines colored by
pressure quantify head loss
in ductwork
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Where is CFD used? (Hydraulics)
• Where is CFD used?
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Aerospace
Appliances
Automotive
Biomedical
Chemical Processing
HVAC&R
– Hydraulics
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Marine
Oil & Gas
Power Generation
Sports
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Where is CFD used? (Marine)
• Where is CFD used?
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Aerospace
Appliances
Automotive
Biomedical
Chemical Processing
HVAC&R
Hydraulics
– Marine
– Oil & Gas
– Power Generation
– Sports
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Where is CFD used? (Oil & Gas)
• Where is CFD used?
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Aerospace
Appliances
Automotive
Biomedical
Chemical Processing
HVAC&R
Hydraulics
Marine
Volume fraction of gas
Flow vectors and pressure
distribution on an offshore oil rig
Volume fraction of oil
Volume fraction of water
– Oil & Gas
Analysis of multiphase
separator
– Power Generation
– Sports
Flow of lubricating
mud over drill bit
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Where is CFD used? (Power Generation)
• Where is CFD used?
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Aerospace
Appliances
Automotive
Biomedical
Chemical Processing
HVAC&R
Hydraulics
Marine
Oil & Gas
Flow around cooling
towers
Flow in a
burner
– Power Generation
– Sports
Flow pattern through a water
turbine.
Pathlines from the inlet
colored by temperature
during standard 15
operating conditions
Where is CFD used? (Sports)
• Where is CFD used?
– Aerospace
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Appliances
Automotive
Biomedical
Chemical Processing
HVAC&R
Hydraulics
Marine
Oil & Gas
Power Generation
– Sports
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Physics
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CFD codes typically designed for representation
of specific flow phenomenon
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Viscous vs. inviscid (no viscous forces) (Re)
Turbulent vs. laminar (Re)
Incompressible vs. compressible (Ma)
Single- vs. multi-phase (Ca)
Thermal/density effects and energy equation (Pr, g, Gr,
Ec)
– Free-surface flow and surface tension (Fr, We)
– Chemical reactions, mass transfer
– etc…
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Physics
Fluid Mechanics
Inviscid
Viscous
Laminar
Compressible
(air, acoustic)
Incompressible
(water)
Turbulence
Internal
External
(pipe,valve)
(airfoil, ship)
Components of Fluid Mechanics
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Navier-Stokes Equation
Claude-Louis Navier
George Gabriel Stokes
D
2

v  p    v   g
Dt
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Modeling
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Mathematical representation of the physical problem
– Some problems are exact (e.g., laminar pipe flow)
– Exact solutions only exist for some simple cases. In
these cases nonlinear terms can be dropped from the NS equations which allow analytical solution.
– Most cases require models for flow behavior [e.g.,
Reynolds Averaged Navier Stokes equations (RANS)
or Large Eddy Simulation (LES) for turbulent flow]
Initial —Boundary Value Problem (IBVP), include:
governing Partial Differential Equations (PDEs), Initial
Conditions (ICs) and Boundary Conditions (BCs)
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Governing Equations (B,S,& L)
(Equations based on “average” velocity)
v 


  ux   u y   uz  0
t x
y
z
Continuity
 u x

u
u
u 
p  


 u x x  u y x  u z x   
   xx   yx   zx   g x
x
y
z 
x  x
y
z 
 t
 
x - Equation of motion
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Numerics / Discretization
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Computational solution of the IBVP
 Method dependent upon the model equations and
physics
 Several components to formulation
– Discretization and linearization
– Assembly of system of algebraic equations
– Solve the system and get approximate solutions
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Finite Differences
 u 
  
 x i , j
  2u  x    3u  x 2
  2 
  3 

 x i , j 2  x i , j 6
ui 1, j  ui , j
x
Finite difference
representation
Truncation error
Methods of Solution
Direct methods
Cramer’s Rule, Gauss elimination
LU decomposition
Iterative methods
Jacobi method, Gauss-Seidel
Method, SOR method
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Numeric Solution
(Finite Differences)
ui 1, j
jmax
j+1
j
j-1
o
2
3
2
3






u
x 
u
x 
 u 




 ui , j    x   2 
 3 

 x i , j
 x i , j 2
 x i , j 6
x
y
i-1 i i+1
Taylor’s Series Expansion
u i,j = velocity of fluid
imax x
Discrete Grid Points
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CFD process
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Geometry description
Specification of flow conditions and properties
Selection of models
Specification of initial and boundary conditions
Grid generation and transformation
Specification of numerical parameters
Flow solution
Post processing: Analysis, and visualization
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Geometry description
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Typical approaches
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– Make assumptions and
simplifications
– CAD/CAE integration
– Engineering drawings
– Coordinates include Cartesian
system (x,y,z), cylindrical system (r,
θ, z), and spherical system(r, θ, Φ)
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Selection of models for flow field
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Direct Numerical Simulations (DNS) is to solve the N-S
equations directly without any modeling. Grid must be fine
enough to resolve all flow scales. Applied for laminar flow
and rare be used in turbulent flow.
Reynolds Averaged Navier-Stokes (NS) equations (RANS)
is to perform averaging of NS equations and establishing
turbulent models for the eddy viscosity. Too many
averaging might damping vortical structures in turbulent
flows
Large Eddy Simulation (LES), Smagorinsky’ constant
model and dynamic model. Provide more instantaneous
information than RANS did. Instability in complex
geometries
Detached Eddy Simulation (DES) is to use one single
formulation to combine the advantages of RANS and LES.
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CFD - how it works
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Analysis begins with a mathematical
model of a physical problem.
Conservation of matter, momentum,
and energy must be satisfied
throughout the region of interest.
Fluid properties are modeled
empirically.
Simplifying assumptions are made in
order to make the problem tractable
(e.g., steady-state, incompressible,
inviscid, two-dimensional).
Provide appropriate initial and
boundary conditions for the problem.
Filling
Nozzle
Bottle
Domain for bottle filling
problem.
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CFD - how it works (2)
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CFD applies numerical methods (called
discretization) to develop approximations of the
governing equations of fluid mechanics in the
fluid region of interest.
– Governing differential equations: algebraic.
– The collection of cells is called the grid.
– The set of algebraic equations are solved
numerically (on a computer) for the flow field
variables at each node or cell.
– System of equations are solved simultaneously
to provide solution.
 The solution is post-processed to extract
quantities of interest (e.g. lift, drag, torque, heat
transfer, separation, pressure loss, etc.).
Mesh for bottle filling
problem.
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Discretization
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Domain is discretized into a finite set of control volumes
or cells. The discretized domain is called the “grid” or the “mesh.”
 General conservation (transport) equations for mass, momentum,
energy, etc., are discretized into algebraic equations.
 All equations are solved to render flow field.

dV   V  dA     dA   S dV
t V
A
A
V
unsteady
convection
Eqn.
continuity
x-mom.
y-mom.
energy
diffusion

1
u
v
h
generation
control
volume
Fluid region of
pipe flow
discretized into
finite set of
control volumes
(mesh).
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Design and create the grid
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Should you use a quad/hex grid, a tri/tet grid, a hybrid grid, or a
non-conformal grid?
What degree of grid resolution is required in each region of the
domain?
How many cells are required for the problem?
Will you use adaption to add resolution?
Do you have sufficient computer memory?
tetrahedron
hexahedron
pyramid
triangle
arbitrary polyhedron
prism or wedge
quadrilateral
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Tri/tet vs. quad/hex meshes
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For simple geometries, quad/hex
meshes can provide high-quality
solutions with fewer cells than a
comparable tri/tet mesh.
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For complex geometries, quad/hex
meshes show no numerical
advantage, and you can save
meshing effort by using a tri/tet
mesh.
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Hybrid mesh example
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Valve port grid.
Specific regions can be meshed with
different cell types.
Both efficiency and accuracy are
enhanced relative to a hexahedral or
tetrahedral mesh alone.
tet mesh
hex mesh
wedge mesh
Hybrid mesh for an
IC engine valve port
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Dinosaur mesh example
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Set up the numerical model
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For a given problem, you will need to:
– Select appropriate physical models.
– Turbulence, combustion, multiphase, etc.
– Define material properties.
 Fluid.
 Solid.
 Mixture.
– Prescribe operating conditions.
– Prescribe boundary conditions at all boundary zones.
– Provide an initial solution.
– Set up solver controls.
– Set up convergence monitors.
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Initial and boundary conditions
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For steady/unsteady flow
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IC should not affect final solution, only convergence path, i.e.
iteration numbers needed to get the converged solution.
Robust codes should start most problems from very crude IC, .
But more reasonable guess can speed up the convergence.
Boundary conditions
– No-slip or slip-free on the wall, periodic, inlet (velocity
inlet, mass flow rate, constant pressure, etc.), outlet
(constant pressure, velocity convective, buffer zone,
zero-gradient), and non-reflecting (compressible flows,
such as acoustics), etc.
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Compute the solution
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The discretized conservation equations are solved iteratively. A
number of iterations are usually required to reach a converged
solution.
 Convergence is reached when:
– Changes in solution variables from one iteration to the next
are negligible.
– Residuals provide a mechanism to help monitor this trend.
– Overall property conservation is achieved.
 The accuracy of a converged solution is dependent upon:
– Appropriateness and accuracy of the physical models.
– Grid resolution and independence.
– Problem setup.
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Numerical parameters & flow
solution
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Typical time
history of
residuals
 The closer the
flow field to the
converged
solution, the
smaller the speed
of the residuals
decreasing.
Solution converged, residuals do
not change after more iterations
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Post-processing
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Analysis, and visualization
– Calculation of derived variables
Vorticity
 Wall shear stress
– Calculation of integral parameters: forces,
moments
– Visualization (usually with commercial software)
 Simple X-Y plots
 Simple 2D contours
 3D contour carpet plots
 Vector plots and streamlines (streamlines are
the lines whose tangent direction is the same
as the velocity vectors)
 Animations (dozens of sample pictures in a
series of time were shown continuously)
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Examine the results
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Visualization can be used to answer such questions as:
– What is the overall flow pattern?
– Is there separation?
– Where do shocks, shear layers, etc. form?
– Are key flow features being resolved?
– Are physical models and boundary conditions appropriate?
– Numerical reporting tools can be used to calculate
quantitative results, e.g:
 Lift, drag, and torque.
 Average heat transfer coefficients.
 Surface-averaged quantities.
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Velocity vectors around a
dinosaur
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Velocity magnitude (0-6 m/s)
on a dinosaur
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Pressure field on a dinosaur
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Advantages of CFD
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Relatively low cost.
– Using physical experiments and tests to get essential
engineering data for design can be expensive.
– CFD simulations are relatively inexpensive, and costs are
likely to decrease as computers become more powerful.
 Speed.
– CFD simulations can be executed in a short period of time.
– Quick turnaround means engineering data can be introduced
early in the design process.
 Ability to simulate real conditions.
– Many flow and heat transfer processes can not be (easily)
tested, e.g. hypersonic flow.
– CFD provides the ability to theoretically simulate any
physical condition.
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Limitations of CFD
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Physical models.
– CFD solutions rely upon physical models of real world
processes (e.g. turbulence, compressibility, chemistry,
multiphase flow, etc.).
– The CFD solutions can only be as accurate as the physical
models on which they are based.
 Numerical errors.
– Solving equations on a computer invariably introduces
numerical errors.
– Round-off error: due to finite word size available on the
computer. Round-off errors will always exist (though they
can be small in most cases).
– Truncation error: due to approximations in the numerical
models. Truncation errors will go to zero as the grid is
refined. Mesh refinement is one way to deal with truncation
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error.
Limitations of CFD (2)
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Boundary conditions.
– As with physical models, the accuracy of the CFD solution
is only as good as the initial/boundary conditions provided to
the numerical model.
– Example: flow in a duct with sudden expansion. If flow is
supplied to domain by a pipe, you should use a fullydeveloped profile for velocity rather than assume uniform
conditions.
Computational
Domain
Computational
Domain
Uniform Inlet
Profile
Fully Developed Inlet
Profile
poor
better
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Software and resources
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CFD software was built upon physics, modeling, numerics.
Two types of available software
– Commercial (e.g., FLUENT, CFX, Star-CD)
– Research (e.g., CFDSHIP-IOWA, U2RANS)
More information on CFD can be got on the following website:
– CFD Online: http://www.cfd-online.com/
– CFD software
 FLUENT: http://www.fluent.com/
 CFDRC: http://www.cfdrc.com/
 Computational Dynamics: http://www.cd.co.uk/
 CFX/AEA: http://www.software.aeat.com/cfx/
– Grid generation software
 Gridgen: http://www.pointwise.com
 GridPro: http://www.gridpro.com/
 Hypermesh
– Visualization software
 Tecplot: http://www.amtec.com/
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THANK YOU
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